Question

A tree casts a shadow that is 9 meters long. A 54 meter tall building nearby casts a shadow that is 24 meters long. What is the height of the tree

Answer 1

Height of the tree is 20.25 m.

Explanation:

Length of building AB = 54 m

Length of tree DE = 9 m

Shadow casted by the building (BC) = 24 m

Shadow casted by the tree (CE) = 9 m

Since, ΔABC ~ ΔDEC

By the property of similar triangles, corresponding sides of the similar triangles will be proportional.

`(AB)/(DE)=(BC)/(EC)`

`(54)/(h)=(24)/(9)`

h =
`(54* 9)/(24)`

h = 20.25 m

Therefore, height of the tree is 20.25 m.